I was curious about the reasoning behind some of their choices. In particular, why the use of set (rather than centroid) distances, and why the choice of mahalanobis (rather than euclidean) metric for measuring grid displacements.

I have seen that spring-based models work quite well for a wide number of engineering applications

The detection of occluded images is important to prove for this type of a model (and is done in the paper experimentally). But they should also have done occluded images of people. Say we only see a person's body and head, it would be quite possible to confuse the person with other objects (like TV on a table). Some of these can be eliminated using the prior probabilities though by restricting the size of the persons.